Question

For the function f(x)

8 Vas - 8. find / -'(X).
9
+8
of-'() = (9)
O/(x) = 9(+8)
O!'(x) = (18)
Of(x) = 9(2+8)
8
Submit Answer

Answer 1

Given:

The function is

`f(x)=\frac{8\sqrt[3]{x}-8}{9}`

To find:

The inverse function
`f^(-1)(x)`.

Solution:

We have,

`f(x)=\frac{8\sqrt[3]{x}-8}{9}`

Step 1: Putting f(x)=y, we get

`y=\frac{8\sqrt[3]{x}-8}{9}`

Step 2: Interchange x and y.

`x=\frac{8\sqrt[3]{y}-8}{9}`

Step 3: Isolate variable y.

`9x=8\sqrt[3]{y}-8`

`9x+8=8\sqrt[3]{y}`

`(9x+8)/(8)=\sqrt[3]{y}`

Taking cube on both sides, we get

`\left((9x+8)/(8)\right)^3=y`

`y=\left((9x+8)/(8)\right)^3`

Step 4: Putting
`y=f^(-1)(x)`, we get

`f^(-1)(x)=\left((9x+8)/(8)\right)^3`

Therefore, the correct option is C.